The sterplot has 10 data points. The data points are in a linear pattern trending down from left to right.

Question

Which of the following equations is the most appropriate linear model for the data shown in the sterplot?

Accepted Answer

Choice B is correct. The equation representing a linear model can be written in the form y = a + b x , or y = b x + a , where b is the slope of the graph of the model and 0 , a is the y -intercept of the graph of the model. The sterplot shows that as the x -values of the data points increase, the y -values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, b < 0 . The sterplot also shows that the data points are close to the y -axis at a positive value of y . Therefore, the y -intercept of the graph of an appropriate linear model has a positive y -coordinate, which means a > 0 . Of the given choices, only choice B, y = - 1.9 x + 10.1 , has a negative value for b , the slope, and a positive value for a , the y -coordinate of the y -intercept. Choice A is incorrect. The graph of this model has a y -intercept with a negative y -coordinate, not a positive y -coordinate. Choice C is incorrect. The graph of this model has a positive slope, not a negative slope, and a y -intercept with a negative y -coordinate, not a positive y -coordinate. Choice D is incorrect. The graph of this model has a positive slope, not a negative slope.

Question the-st